A Public folder sychronization job fails with the following lines within the target log:
The Migration Manager Public Folder Migration Administrator Mailbox is NOT associated with a “primary” Public Folder hierarchy mailbox on the target Exchange 2013.
Setting the association between the Migration Manager Public Folder Migration Administrator Mailbox and the "Primary" Public Folder Hierarchy Mailbox should resolve the issue.
To set such an association, please run the following cmdlet in Exchange shell:
Set-Mailbox –Identity <Public_Folder_Migration_Administrator_Mailbox> -DefaultPublicFolderMailbox <Primary_Hierarchy_Mailbox>
To find out the name of the Migration Manager Public Folder Migration Administrator Mailbox, expand the Target Exchange Organization in Migration Manager Tree down to the Exchange server selected as the target for Public Folder migration, right-click it and select Properties from the shortcut menu. On the Connection page check the Public Folder Migration Administrator Mailbox field.
To find out the GUID of the Primary Hierarchy Mailbox, you can run Get-OrganizationConfig | FL RootPublicFolderMailbox or check its name in Exchange 2013 Admin Center.